TOWNSVILLE CATHOLIC EDUCATION OFFICE – MATHEMATICS SCOPE AND SEQUENCE
NUMBER AND ALGEBRA
Year 10
Term 1
Term 2
Term 3
Term 4
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Substitute values into formulas to determine an unknown. Represent word problems with simple
linear equations and solve them to answer questions (ACMNA234) TIMESNA36
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Solve problems involving linear equations, including those derived from formulas involving
rearrangement (ACMNA235) TIMESNA26 TIMESNA36
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Solve linear inequalities and graph their solutions on a number line (ACMNA236)
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Solve problems involving parallel and perpendicular lines (ACMNA238) TIMESNA29
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Explore the connection between algebraic and graphical representations of simple quadratics,
rectangular hyperbolas, circles and exponential functions using digital technology as appropriate
including those that have undergone a single transformation. Sketch the graphical
representation of parabolas, exponential functions and circles (ACMNA239) TIMESNA35
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Term 1
Term 2
Term 3
Term 4
Solve problems involving surface area and volume of right pyramids, right cones, spheres and
related composite solids. Use formulas to solve problems including authentic situations
(ACMMG271) TIMESMG12
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Formulate proofs involving congruent triangles and angle properties (ACMMG243) TIMESMG22
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Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical
exercises involving plane shapes. Present reasoned arguments and apply an understanding of
relationships to deduce properties of geometric figures (ACMMG244) TIMESMG20 TIMESMG21
TIMESMG22
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Solve right-angled triangle problems including those involving direction and angles of elevation
and depression (ACMMG245) TIMESMG23
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Sub-Strand
Money and Financial Mathematics
Patterns and Algebra
Linear and non-linear relationships
Connect the compound interest formula to repeated applications of simple interest
using appropriate digital technologies. Calculate compound interest and solve related problems
(ACMNA229) TIMESNA22
Factorise algebraic expressions by taking out a common algebraic factor including those where a
common factor is an algebraic expression
eg. 2𝑥𝑦 2 + 6𝑥 2
= 2𝑥(𝑦 2 + 3𝑥) and
a𝑥 + a𝑦 + b𝑥 + b𝑦
= a(𝑥 + 𝑦) + b(𝑥 + 𝑦)
= (𝑥 + 𝑦)(a + b)
(ACMNA230) TIMESNA33
Simplify algebraic products and quotients. Apply knowledge of index laws to algebraic terms, and
simplifying algebraic expressions using both positive and negative integral indices (ACMNA231)
TIMESNA32
Apply the four operations to simple algebraic fractions with numerical denominators
𝑥
𝑥
5𝑥
eg. + = . Solve a wide range of linear equations, including those involving one or two
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simple algebraic fractions, and check solutions by substitution (ACMNA232) TIMESNA25
TIMESNA26
Expand binomial products and factorise monic quadratic expressions using a variety of strategies.
Use expansion patterns for the special binomial products (a + b)(a - b) and (a ± b)2 inversely to
factorise quadratic expressions. Use the area model inversely to factorise quadratic expressions
of the form a𝑥 2 + b𝑥 + c, where a= ±1. Explore the method of completing the square to factorise
quadratic expressions and solve quadratic equations (ACMNA233) TIMESNA33
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Solve linear equations involving simple algebraic fractions eg.
+ = 1. Represent word
𝑥+1
𝑥
problems, including those involving fractions, as equations and solving them to answer the
question (ACMNA240) TIMESNA25
Solve simple quadratic equations using a range of strategies. Identify the connection between
algebraic and graphical solutions of equations (eg. understanding that the x-intercepts are the
solutions of f(x) = 0). Explore the method of completing the square to factorise quadratic
expressions and solve quadratic equations (ACMNA241) TIMESNA34 TIMESNA35
MEASUREMENT AND
GEOMETRY
Using Units of Measurement
Geometric Reasoning
Pythagoras and Trigonometry
Year 10
STATISTICS AND PROBABILITY
Year 10
Term 1
Term 2
Term 3
Term 4
Chance
Describe the results of two- and three-step chance experiments, both with and without
replacements, assign probabilities to outcomes and determine probabilities of events. Investigate
the concept of independence. Recognise that some sets of chance events are dependent on a
previous result and others are not, that this distinction is important when calculating
probabilities, and that events are independent if P(A) x P(B) = P(A and B) (ACMSP246) TIMESSP15
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Use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements
and identify common mistakes in interpreting such language (ACMSP247) TIMESSP15
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Determine quartiles and interquartile range. Find the five-number summary (minimum and
maximum values, median and upper and lower quartiles) and using its graphical representation,
the box plot, as tools for both numerically and visually comparing the centre and spread of data
sets (ACMSP248) TIMESSP08
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Construct and interpret box plots and use them to compare data sets (ACMSP249) TIMESSP08
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Compare shapes of box plots to corresponding histograms and dot plots (ACMSP250) TIMESSP08
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Use scatter plots to investigate and comment on relationships between two continuous variables,
making comparisons and drawing conclusions (ACMSP251) TIMESSP08
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Investigate and describe bivariate data (data relating to two variables, eg. arm span and height)
numerical data where the independent variable is time (ACMSP252) TIMESSP08
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Evaluate statistical reports in the media and other places by linking claims to displays, statistics
and representative data (ACMSP253) TIMESSP08
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Data representation and interpretation